What this calculator does
Converting a fraction to a percentage is a matter of dividing the numerator by the denominator and multiplying by 100: 3/8 becomes 37.5%. This calculator also runs the conversion the other way, taking a percentage such as 37.5% and returning it as a simplified fraction, 3/8, which is a step people more often reach for a calculator to do by hand.
The reverse direction is where mistakes creep in. Percentages that are not round numbers, like 37.5% or 12.5%, need to be scaled up by a power of 10 before the fraction can be simplified with the greatest common divisor, and it is easy to simplify too early or too late and land on the wrong fraction.
The formula
Fraction to percentage divides the numerator by the denominator and multiplies by 100. Percentage to fraction does the reverse: the percentage is placed over 100, then both are scaled up by powers of 10 until the numerator is a whole number (to handle decimal percentages like 37.5%), before the pair is reduced using their greatest common divisor.
| Term | Meaning |
|---|---|
| Numerator | The top number of a fraction, being converted into a percentage. |
| Denominator | The bottom number of a fraction; the total the numerator is being compared against. |
| Simplified fraction | A fraction reduced so its numerator and denominator share no common factor above 1. |
The inputs explained
| Field | What to enter |
|---|---|
| Convert | Choose which direction to convert: a fraction into a percentage, or a percentage back into a fraction. |
| Numerator (fraction to percentage only) | The numerator of the fraction, used only when converting fraction to percentage. |
| Denominator (fraction to percentage only) | The denominator of the fraction, used only when converting fraction to percentage. |
| Percentage (percentage to fraction only) | The percentage to convert back to a fraction, used only when converting percentage to fraction. |
When to use it
Marking a test or survey result
A score reported as "17 out of 20" is easier to compare against other results once it is expressed as a percentage, and this calculator handles that conversion directly from the raw fraction.
Reading a percentage back as a ratio
A discount, interest rate or probability quoted as a percentage, such as 12.5%, is sometimes easier to reason about as the plain fraction 1/8, particularly when it needs to be applied to a physical quantity that only comes in whole units.
Checking simplification by hand
When a fraction to percentage conversion or its reverse is done manually, running the same numbers through this calculator confirms whether the fraction was simplified correctly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What percentage is a given fraction?
A spread of fractions with the same denominator, each converted to a percentage.
| Numerator (over a denominator of 8) | Percentage | As a decimal |
|---|---|---|
| 1 | 12.5% | 0.1250 |
| 2 | 25.0% | 0.2500 |
| 3 | 37.5% | 0.3750 |
| 4 | 50.0% | 0.5000 |
| 5 | 62.5% | 0.6250 |
| 6 | 75.0% | 0.7500 |
| 7 | 87.5% | 0.8750 |
What fraction is a given percentage?
A spread of percentages, each converted back to its simplest fraction form.
| Percentage | Fraction | As a decimal |
|---|---|---|
| 12.5% | 1/8 | 0.1250 |
| 25% | 1/4 | 0.2500 |
| 37.5% | 3/8 | 0.3750 |
| 50% | 1/2 | 0.5000 |
| 62.5% | 5/8 | 0.6250 |
| 75% | 3/4 | 0.7500 |
| 87.5% | 7/8 | 0.8750 |
Questions
How do I convert a fraction to a percentage without a calculator?
Divide the numerator by the denominator to get a decimal, then move the decimal point two places to the right (which is the same as multiplying by 100). For 3/8, that is 0.375, then 37.5%.
Why does my percentage not simplify to a neat fraction?
Some percentages, particularly ones with several decimal places, come from fractions with large or unusual denominators that do not reduce to small whole numbers. The simplification is still correct; the underlying fraction is just not a tidy one.
Can the denominator be zero?
No. Dividing by a zero denominator is undefined, so this calculator will not return a percentage for a fraction written with a denominator of 0.
What is the difference between this and the percentage calculator?
The percentage calculator answers everyday questions like "X% of Y" or "X increased by Y%"; this page is specifically about translating between the fraction and percentage representations of the same value, in either direction.
For the everyday percentage-of-a-number and percentage-increase questions, see the percentage calculator. To add, subtract, multiply or divide fractions directly, use the fraction arithmetic calculator.